Spectral stability of the Coulomb–Dirac Hamiltonian with anomalous magnetic moment

Abstract

We show that the point spectrum of the standard Coulomb–Dirac operator H 0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H a as the anomaly parameter tends to 0. For negative angular momentum quantum number κ, this holds for all Coulomb coupling constants c for which H 0 has a distinguished self-adjoint realisation. For positive κ, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H 0 and the limits of eigenvalues of H a appears, accompanied with additional oscillations of the eigenfunctions of H a very close to the origin.